Ok, I played around a bit more and found a way to set up the desktops quickly without wreaking chaos.
It now actually works windowed/desktop resolution with both desktops active and in native resolution. Turns out, the taskbar even affects winSP when it is on the
other desktop (had to drag it over to the primary), as well as "always on top" had to be on (in addition to autohie off). Still a bit of preparation each time I want to play, but it's worth it.
Thanks for the detailed help, I'm a bit too rusty in dealing with all those quirks of older games.